Felipe Castillo

Boundary observers for linear and quasi-linear hyperbolic systems with application to flow control

In this paper we consider the problem of boundary observer design for one-dimensional first order linear and quasi-linear strict hyperbolic systems with n rightward convecting transport PDEs. By means of Lyapunov based techniques, we derive some sufficient conditions for exponential boundary observer design using only the information from the boundary control and the boundary conditions. We consider static as well as dynamic boundary controls for the boundary observer design. The main results are illustrated on the model of an inviscid incompressible flow.

Simultaneous Air Fraction and Low-Pressure EGR Mass Flow Rate Estimation for Diesel Engines

Abstract This paper describes a low-pressure exhaust gas recirculation (LP-EGR) mass flow rate estimation method and a robust air mass fraction observer for a Diesel engine with dual-loop EGR system. Both observers operate simultaneously eliminating the need for pressure measurement upstream the LP-EGR valve. A sliding mode observer is designed to estimate the LP-EGR mass flow rate using the standard sensors available in commercial Diesel engines. A robust linear parameter varying Kalman filter is designed for the air mass fraction estimation. The convergence and robustness of the observers are ensured by means of Lyapunov stability and a linear matrix inequality (LMI) framework for the sliding mode observer and robust Kalman filter, respectively. The observers are evaluated with a Motor Vehicle Emission Group (NMVEG) cycle using an engine model validated on an experimental benchmark as a reference.

Dynamic boundary stabilization of linear and quasi-linear hyperbolic systems

Systems governed by hyperbolic partial differential equations with dynamics associated with their boundary conditions are considered in this paper. These infinite dimensional systems can be described by linear or quasi-linear hyperbolic equations. By means of Lyapunov based techniques, some sufficient conditions are derived for the exponential stability of such systems. A polytopic approach is developed for quasi-linear hyperbolic systems in order to guarantee stability in a region of attraction around an equilibrium point, given specific bounds on the parameters. The main results are illustrated on the model of an isentropic inviscid flow.

Fresh Air Fraction Control in Engines Using Dynamic Boundary Stabilization of LPV Hyperbolic Systems

In this paper, we consider the boundary control of the fresh air mass fraction in a Diesel engine operated with low-pressure exhaust gas recirculation. The air mass fraction transport phenomenon is modeled using a cascade of first-order linear parameter-varying hyperbolic systems with dynamics associated with their boundary conditions. By means of Lyapunov-based techniques, sufficient conditions are derived to guarantee the exponential stability of this class of infinite dimensional systems. We develop a polytopic approach to synthesize a robust boundary control that guarantees the exponential stability for a given convex parameter set. Simulation results illustrate the effectiveness of the proposed boundary control to regulate the mass fraction of fresh air in a Diesel engine.

Dynamic Boundary Stabilization of Linear Parameter Varying Hyperbolic Systems: Application to a Poiseuille Flow

The problem of boundary control in first order linear parameter varying (LPV) hyperbolic systems with dynamics associated with the boundary conditions is considered in this article. By means of Lyapunov based techniques, some sufficient conditions are derived for the exponential stability of these infinite dimensional systems. A polytopic approach is developed in order to synthesize a robust boundary control which guarantees the exponential stability for a given convex parameter set. An application using a Poiseuille flow control experimental setup illustrates the main results.

Exhaust Manifold Pressure Estimation Diesel Equipped with a VGT Turbocharger

This paper develops an exhaust manifold pressure estimation method for a Diesel engine equipped with a variable geometry turbine (VGT) turbocharger. Extrapolated VGT data-maps are used directly for the estimation of the exhaust pressure using a non-iterative Newton-Raphson based method suitable for real-time applications. This approach can give more accurate estimations than traditional methods because it takes into account the turbine speed effect on the turbine mass flow rate. All this without increasing the calculation load significantly. The proposed exhaust manifold estimation can be used to relieve the exhaust manifold pressure physical sensor during engine operating conditions where its reliability is low. The estimator is evaluated in transient with two different engine cycles using a engine model validated in a benchmark as a reference.

Restriction Model Independent Method for Non-Isentropic Outflow Valve Boundary Problem Resolution

To meet the new engine regulations, increasingly sophisticated engine alternative combustion modes have been developed in order to achieve simultaneously the emission regulations and the required engine drivability. However, these new approaches require more complex, reliable and precise control systems and technologies. The 0-D model based control systems have proved to be successful in many applications, but as the complexity of the engines increases, their limitations start to affect the engine control performance. One of the 0-D modeling limitations is their inability to model mass transport time. 1-D modeling allows some of the 0-D models limitations to be overcome, which is the motivation of this work. In this paper, two quasi-steady outflow boundary models are developed: one is based on the isentropic contraction and the other on a momentum conservation approach. Both are compared with computational fluid dynamics (CFD) 3-D simulations. Then, an innovative method for solving the outflow boundary problem taking into account the entropy correction at the boundary for a 1-D unsteady gas flow modeling is presented. Its formulation allows more predictive quasi-steady models to be included in the boundary resolution scheme by solving the boundary problem independently of the restriction model. It means that a physical restriction model can be modified without needing to change the boundary resolution method. A Newton-Raphson algorithm is used with a modified Method of Characteristics (MOC) scheme to solve the boundary problem along with an extrapolation for the initialization of the scheme, which reduces the amount of iterations required and increases the solution accuracy. The unsteady behavior of the method is illustrated in an engine intake valve example where the numerical performance of the proposed method is compared with the numerical scheme presented in the literature. Finally, the proposed method for solving the unsteady state is validated using 3-D CFD simulations as a reference.

Intra-Pipe Restriction Non-Homentropic Boundary Resolution Method

A complete non-homentropic boundary resolution method for a flow upstream and downstream an intrapipe restriction is considered in this article. The method is capable of introducing more predictable quasi-steady restriction models into the boundary problem resolution without adding artificial discharge coefficients. The traditional hypothesis of isentropic contraction, typically considered for the boundary resolution, is replaced by an entropy corrected method of characteristics (MOC) in order to be consistent with a non-homentropic formulation. The boundary resolution method is designed independently of the quasi-steady restriction models which allows obtaining a greater modeling flexibility when compared with traditional methods. An experimental validation at unsteady conditions is presented using different restriction quasi-steady models to illustrate the effectiveness of the proposed boundary resolution method in terms of predictability as well as flexibility.

Dynamic Boundary Stabilization of First Order Hyperbolic Systems

In this chapter, we address the problem of the dynamic boundary stabilization of linear, quasilinear and LPV first-order hyperbolic systems. We provide sufficient conditions for the exponential stability for this class of infinite dimensional systems by means of Lyapunov based techniques and matrix inequalities. We develop an applicative example of a temperature boundary control in a Poiseuille flow using some of our main results and we present simulation results that illustrate the efficiency of our approach.